How to use my own geometry as mesh deform cage in BlenRig add-on?
Yes, Although you may end up needing to spend just as much time correcting the weights.

The data transfer modifier can copy vertex weights, but you will probably need to do some tweaking after and of the modifier settings to get things right. It will also need the blenrig cage to be made to at least roughly match your new cage, as you are going to want to use the "Nearest Vertex" setting.